Feral Druid's strengths are animal forms. In despite of that, you'll occasionally find one who's too scared to enter melee and does a lot of root/moonfire spam. You can use the moonkin strategy against them.
If they're silly enough to go cat form for a significant part of the fight, beat them up like you would a rogue. Most feral druids won't stay cat, though; they build combo points to get a bleed effect on you, then switch to bear or root you to pop some moonfires (n00bz omg). If you have a good two-hander you're itching to use, a cat form druid makes one of the best targets.
A bearform Druid is tough to hurt, so use Rend and make sure to keep it on. Also make sure to keep Hamstring on; although they can shift out of it, it's not mana efficient to do so when you're just going to hamstring them again when they switch back, so most will suffer through the snare and you'll have an advantage.
As usual Battle Stance is best (for Rend/Hamstring/Overpower), but remember that Druids have Frenzied Regeneration and can also heal pretty much whenever they want by shifting back to caster and rooting you (roots will outlast any silences/fears/etc). You can employ, and popping your PvP trinket will just get you rooted again in a few seconds). If both of your life bars are going down at a close to even rate, it may be best to switch to Defensive and spam shield block. The lost DPS will make the battle take longer, giving the druid more time to regen mana between heals, but sometimes you need to do it.
Try to store rage late in the fight. If the Druid waits until he's too low on health to switch back to caster and root you (low enough that you should be able to kill him if he doesn't get to heal), pop a Concussion Blow or Intimidating Shout ASAP to keep him in place and yourself unrooted. Bandage, but before the stun/fear wears off, hit him with whichever of CB or Int. Shout you didn't use if you have the rage, or shield bash (you have Improved, right?). That'll buy you some more time to set up for the kill. If, by chance, you get rooted but still stun him, keep him immobilized however you can and hope for an early root break.
If you and the Druid are equally geared, or if he's better geared, you'll probably want to sunder him in bear form. Be very cognizant of how long it's been since you last landed a sunder, though- once five are up, you only need one every thirty seconds to keep them there, so the last thing you want is to have to put all five back on again.
Moonkin Druids are essentially mages with lower burst damage but higher armor. All they're going to do is root and moonfire spam you.
Use your PvP trinket immediately to kill the longest-duration root, get in close, and try to survive until they can't root you anymore. On subsequent roots, use CB or Int. Shout to keep them from taking maximum advantage of your rooted state.
Use shield bash for the silence effect to buy yourself time. If you can hit them while rooted, they'll get away, but it'll give you a few seconds of not getting nuked. If you hit them before they cast roots, that's a few seconds you get of whacking them in the face. And if you interrupt a root cast (takes some luck, as many druids will use Nature's Grasp to root you when you hit them as opposed to casting the spell), that's six seconds before they can cast it again.
Moonkin can't heal. Much like with a feral druid, if they switch to caster at dangerously low health, do what you can to stop them from healing until you get the kill. If they switch out and there's no way you can stop them long enough to get them down, try to get one heal interrupt off if possible so you have more time to hit them in lower-armor caster form.
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